Potential of a conductor in a non-uniform E field

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SUMMARY

The discussion centers on the potential of a conducting rod placed in a non-uniform electric field created by a point charge. It is established that the potential throughout the conductor must remain constant, despite the differing potentials at its ends, V_A (10V) and V_B (5V). The conducting rod will have a uniform potential equal to the average of V_A and V_B, which is 7.5V. This conclusion is based on the principle that there can be no net electric field within a conductor in electrostatic equilibrium.

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imagine there is a positive pt charge somewhere in space. so the E field due to this pt charge, falls off with distance.


now, i place a conducting rod parallel to the field some distance away,
such that one end of the rod is at V_A and another end is V_B
(where V_A > V_B)

we also know that there can be no net E-field in a conductor. so potential must be constant throughout a conductor.

my question is. what is the potential?? V_A or V_B? or what?
 
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The potential of the conducting rod will be constant. One end will not be at a different potential to the other end.
-charge (electrons) will be attracted to the end nearest the + charge and the end further from the + charge will be + charged.
 
Yes I know the mechanism.

My question is what is the numerical potential?

Assume the potential due to the external field at pt A is 10V,
the potential due to the external field at pt B is 5V,

then what is the potential anywhere in the rod?
 

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